There is a great explanation at https://vocalprocess.co.uk/singing-teacher-vocal-coach/. In brief, a singing teacher works on vocal technique whilst a coach works on repertoire for performance. I pride myself on my ability to cover both areas.
To quote Vocal Process " These are teachers who understand vocal function on a very deep level, can listen to your voice, take it apart and give you precise technical input to improve it immediately, in one shot or lesson after lesson." That's me!
"Vocal coaches can cover many things including musical style, phrasing, memorising, acting or atmosphere intent, finding your version of the song, choosing music for a set, audition technique and even go as far as advice on your “look”. " "As with the singing teacher, the really skilled vocal coach can listen to you speak or sing and identify your strengths, help you find an authentic performance, and give you targeted, personalised performance techniques to help you find the best version for (and of) you."
Unless you have experience, you don't know, and that's the problem. Anyone can set themselves up as a singing teacher. If they have a professional looking website and some marketing skill you can end up spending a lot of your hard-earned cash and not really learn much.
Check out any claims made. Remember, there are no laws governing who can teach singing! Online searches can help. Don't be afraid to ask questions - if you are not satisfied with the answer, look elsewhere. Use your gut instinct - a good teacher needs to have good people skills. Ideally, you should like them and trust them.
Look out for membership of professional organisations. I am a member of The British Voice Association, The Association of Teachers of Singing and The Incorporated Society of Musicians. Membership of the ISM and the Musician's Union gives you Public Liability Insurance which is essential for a private teacher.
Ask about their training. If they are teaching in the same way that they themselves were taught, be careful. This could mean that you are being taught in a way that is now seriously out-of-date.
Sometimes, people who just love singing or pianists/piano teachers will offer lessons. Maybe choral leaders/conductors will offer their choir private lessons. If you are singing songs all the way through with no actual technical advice or practical solutions to your vocal problems, then you are having coaching - not a singing lesson!
Your teacher may have had a long-standing career as a professional singer. This is definitely a good thing and I believe preferable to a teacher who is not a singer themselves. However, being able to sing yourself is not the same as being a good teacher. One of my best teachers was an accompanist to a well-known singing teacher for many years. From his partnership with her, he learned all her skills and techniques for training a voice plus he was an amazing pianist with a phenomenal knowledge of classical repertoire. Will Hancox, I salute you!
Yes and no! A had a semi-pro singer who came for his first lesson and I was able to help him belt out some top notes comfortably for the first time. He was delighted naturally! However, at his next lesson he admitted that he could not reproduce the notes in the same easy way as he had done in the lesson.
This is fairly typical. As I've said before, the voice is a combination of muscle movements and to co-ordinate them successfully time after time takes PRACTICE!! That is what lessons are for - to guide you over a period of time until you are able to achieve great singing by yourself.
If the student had been a professional who had already trained his voice to a high level of competency, one lesson to tweak what he was doing would have probably been enough.
A classic question! If I had a pound for every time I've been asked this...!
This question tells me a lot about someone. Often, it means that they are looking for a quick fix and are not seriously committed to practice. There is no magic, one-size-fits-all formula for success. Any new skill takes time, practice and patience.
If you have natural singing ability and no bad habits then you may find you improve quickly. If you are not a great singer to start with and have adopted harmful singing strategies over a period of time, there can be some unpicking to do. Muscle memory and habit are powerful - once they have become entrenched they can take some time to undo.
Ask yourself what is it you really want from your voice. Are you prepared to work at it? Give yourself a realistic time-frame and a budget, and commit yourself to regular practice. And of course, remember to enjoy the ride!